Inferential Statistics Chapter 5 Inferential Statistics a b m Chapter 5

Inferential Statistics Population (parameter) Sample (statistics) Discuss the fact that researchers gather data on a sample and then desire to generalize to a population. Use the Neilson television rating system or presidential polls as examples Chapter 5

Thursday evening news… “There they are again! The most terrifying five words in television.” “According to a NEW study….”

????? Hypotheses Research (words) Null (Ho) Alternative (H1) Differentiate between the three different types of hypotheses that can be written The research hypothesis is a statement of a perceived relationship between two variables (e.g., X and Y) The null hypothesis is a statistical hypothesis of NO relationship between the variables. It is often the opposite of the research hypothesis. The alternative hypothesis is what is believed if the null hypothesis is rejected. The alternative hypothesis reflects what is stated in the research hypothesis (I.e., there IS a relationship between the variables). Chapter 5

Hypothesis Testing Research hypothesis of relationship Statistical null hypothesis Alternative hypothesis Obtain data Make decision based on probability The research method follows these steps No matter how sophisticated and involved the statistical test might be, this general process is followed. Chapter 5

Normal Distribution

The Null & Alternative Hypotheses The Null hypothesis Note that when the null hypothesis is true, there is much overlap in the two curves. When the alternative hypothesis is true, the two curves will be separated from one another. The Alternative hypothesis Chapter 5

Are there any Differences in Water Purity? l s D e n v r B o t l e d H2O T a m p This is an example of ANOVA where the researcher was interested in the purity of water. Ask the students to identify the null and alternative hypotheses Chapter 5

Figure 5.1 Type I and Type II Errors True state in population Your decision Ho is true H1 is false Ho is false H1 is true Type I error (alpha) Correct decision Decision Type II error (beta) Reject Ho , accept H1 Differentiate between Type I and Type II errors and provide examples of such. Relate this to the normal distribution and the .05 and.01 alpha level (I.e., probability or level of significance) Accept Ho , reject H1 Chapter 5

Table 5-2 Variable Classification Independent Dependent Presumed cause Presumed effect The antecedent The consequence Manipulated or measured Outcome (measured) by researcher Predicted from Predicted to Predictor Criterion X Y Discuss these different names for the independent and dependent variables Chapter 5

Null Hypothesis DV Control Experimental The small horizontal line represents the Mean. The vertical line represents the variance Note that the Means are exactly the same value on the DV so the Null hypothesis would be true here Control Experimental Chapter 5

Anything Happening Here? DV Note that the Means are somewhat different but not greatly so. Therefore, you probably would continue to believe that the Null hypothesis is true Control Experimental Chapter 5

Anything Happening Here? DV Notice the great variability between the groups relative to the variability within the groups. Note that the Means are very much different from one another so you would reject the Null hypothesis and entertain the alternative hypothesis as the true state of circumstances Control Experimental Chapter 5

Are there any Differences in Water Purity? l s D e n v r B o t l e d H2O T a m p This is an example of ANOVA where the researcher was interested in the purity of water. Ask the students to identify the null and alternative hypotheses. You might briefly mention multiple comparison tests tat this point if the omnibus (overall) ANOVA is significant. Chapter 5

Selected Statistical Tests Chi-Square t-Test for Two Independent Groups Dependent t test for Paired Groups One-Way ANOVA Introduce the statistical tests that will be presented. Indicate that tests of hypotheses are the same for each procedure. However, you have to decide which statistical test to use. That is determined by the number and nature of Independent and Dependent Variables. Chapter 5

What Analysis? IV DV Statistical Test 1 Nominal Chi-Square (2 groups) 1 continuous t-test (>2 groups) One-Way ANOVA

Some Examples Chi-Square Gender and knee injuries in collegiate basketball players Independent t-test Differences in girls and boys Dependent t-test Pre and Post measurement One-Way ANOVA Return to the purity of Water example Indicate that the following slides will present brief examples of each of the statistical tests just presented. Ask the students to identify the IV and DV in each case Ask them to identify the research, null, and alternative hypotheses Chapter 5

Chi Square Example for 6 Conferences (Based on Sports Illustrated, February 13, 1995) Women Men ACC 20 4 Big East 9 SEC 15 5 Big 10 7 Big 8 10 1 PAC 10 14 Total 83 26 109 This Chi-Square example is based on true data published in Sports Illustrated. The numbers have been modified slightly to make the example more clear for students. The assumption is made that there 10 tams in a league and 15 players on a team. Obviously this is not the case in the “Big Eight”, etc. The hypothesis under investigation here is whether there is a relationship between gender and knee injury significant enough to require surgery in college-age basketball players. 10 teams per league * 15 players per team * 6 leagues = 900 players 109/1800 = .06 = 6% injury overall injury rate Chapter 5

Null Hypothesis 846 54 Gender Women Men No 1692 Injury Yes 108 900 900 If the Null hypothesis is true that there is NO relationship between gender and injury requiring knew surgery and the overall injury rate is 6%, you would expect to find this as the distribution of gender and injury rates. In this case you would continue to believe that the null is true 900 900 1800 DF = 1 Chi-Square = 0.00 P < 1.00 Chapter 5

Actual Data 817 874 83 26 Gender Women Men No 1691 Injury Yes 109 900 The actual data, however, suggest that there is a relationship between gender and injury requiring knee surgery. Point out that they should think of the Chi-Square similar to a Z value and that having a high Chi-Square is way out on the distribution and thus VERY UNLIKELY to occur IF the Null hypothesis is true. Thus, you reject the Null hypothesis and entertain the alternative hypothesis that there is a relationship between gender and injury requiring knee surgery 900 900 1800 DF = 1 Chi-Square = 31.73 P < .0001 Chapter 5

An Independent t-test Example G I R L S B O Y S Illustrate how the hypothesis here is a test of two groups (Only ONE IV – Gender – with two groups – girls and boys). As the class to determine what the DV might be – It must be a continuous variable. Chapter 5

A Dependent t-test Example Post Pre Illustrate how the hypothesis here is a Dependent t-test of two groups because the SAME people appear in each group As the class to determine what the DV might be – It must be a continuous variable. Chapter 5

Are there any Differences in Water Purity? l s D e n v r B o t l e d H2O T a m p Return again to the water purity example and point out that this is a One-Way ANOVA because of the number of levels of the Independent Variable. Point out there is ONLY ONE IV here (Water source) but that it has 4 different LEVELS. Ask the students to determine what the DV variable actually is. It is “purity” but purity can be defined in a variety of different ways. Chapter 5

SPSS Examples